Home » date » 2007 » Nov » 21 » attachments

Workshop 3 Q3

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 21 Nov 2007 15:03:55 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw.htm/, Retrieved Wed, 21 Nov 2007 22:57:32 +0100

User-defined keywords:

Seasonal dummies

Dataseries X:

» Textbox « » Textfile « » CSV «

523 0 519 1 509 1 512 1 519 0 517 0 510 1 509 1 501 0 507 1 569 0 580 0 578 1 565 1 547 0 555 0 562 0 561 0 555 1 544 1 537 1 543 1 594 1 611 0 613 1 611 1 594 1 595 0 591 0 589 0 584 1 573 1 567 0 569 1 621 0 629 0 628 1 612 1 595 1 597 0 593 1 590 0 580 1 574 1 573 1 573 1 620 0 626 0 620 1 588 1 566 1 557 0 561 1 549 1 532 1 526 1 511 1 499 1 555 0 565 1 542 1

Text written by user:

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 601.951152073733 + 1.24423963133640x[t] -18.9880184331796M1[t] -24.1953917050691M2[t] -40.7465437788018M3[t] -39M4[t] -37.2488479262673M5[t] -41M6[t] -50.9953917050691M7[t] -57.9953917050691M8[t] -64.8976958525346M9[t] -64.9953917050692M10[t] -10.4000000000000M11[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	601.951152073733	15.458534	38.9397	0	0
x	1.24423963133640	12.678314	0.0981	0.92223	0.461115
M1	-18.9880184331796	22.153819	-0.8571	0.395649	0.197825
M2	-24.1953917050691	23.831633	-1.0153	0.315071	0.157535
M3	-40.7465437788018	22.867873	-1.7818	0.081105	0.040552
M4	-39	21.565559	-1.8084	0.076805	0.038402
M5	-37.2488479262673	21.714118	-1.7154	0.092718	0.046359
M6	-41	21.565559	-1.9012	0.063291	0.031646
M7	-50.9953917050691	23.831633	-2.1398	0.037481	0.01874
M8	-57.9953917050691	23.831633	-2.4335	0.018725	0.009362
M9	-64.8976958525346	22.153819	-2.9294	0.005183	0.002592
M10	-64.9953917050692	23.831633	-2.7273	0.008892	0.004446
M11	-10.4000000000000	21.565559	-0.4823	0.63182	0.31591

Multiple Linear Regression - Regression Statistics
Multiple R	0.547179904465269
R-squared	0.299405847850621
Adjusted R-squared	0.124257309813276
F-TEST (value)	1.70943960598051
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	0.0943120423223625
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	34.0981432300322
Sum Squared Residuals	55808.8018433179

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	523	582.963133640553	-59.9631336405528
2	519	579	-59.9999999999999
3	509	562.448847926267	-53.4488479262673
4	512	564.195391705069	-52.1953917050690
5	519	564.702304147465	-45.7023041474655
6	517	560.951152073733	-43.9511520737328
7	510	552.2	-42.2
8	509	545.2	-36.2
9	501	537.053456221198	-36.0534562211981
10	507	538.2	-31.2000000000000
11	569	591.551152073733	-22.5511520737328
12	580	601.951152073733	-21.9511520737327
13	578	584.20737327189	-6.20737327188945
14	565	579	-14
15	547	561.204608294931	-14.2046082949309
16	555	562.951152073733	-7.95115207373274
17	562	564.702304147465	-2.70230414746545
18	561	560.951152073733	0.0488479262672605
19	555	552.2	2.80000000000001
20	544	545.2	-1.19999999999999
21	537	538.297695852535	-1.29769585253455
22	543	538.2	4.80000000000003
23	594	592.795391705069	1.20460829493088
24	611	601.951152073733	9.04884792626725
25	613	584.20737327189	28.7926267281105
26	611	579	32
27	594	562.448847926267	31.5511520737327
28	595	562.951152073733	32.0488479262673
29	591	564.702304147465	26.2976958525345
30	589	560.951152073733	28.0488479262673
31	584	552.2	31.8
32	573	545.2	27.8
33	567	537.053456221198	29.9465437788018
34	569	538.2	30.8
35	621	591.551152073733	29.4488479262673
36	629	601.951152073733	27.0488479262673
37	628	584.20737327189	43.7926267281105
38	612	579	33
39	595	562.448847926267	32.5511520737327
40	597	562.951152073733	34.0488479262673
41	593	565.946543778802	27.0534562211982
42	590	560.951152073733	29.0488479262673
43	580	552.2	27.8
44	574	545.2	28.8
45	573	538.297695852535	34.7023041474654
46	573	538.2	34.8
47	620	591.551152073733	28.4488479262673
48	626	601.951152073733	24.0488479262673
49	620	584.20737327189	35.7926267281105
50	588	579	9
51	566	562.448847926267	3.55115207373273
52	557	562.951152073733	-5.95115207373274
53	561	565.946543778802	-4.94654377880181
54	549	562.195391705069	-13.1953917050691
55	532	552.2	-20.2
56	526	545.2	-19.2
57	511	538.297695852535	-27.2976958525345
58	499	538.2	-39.2
59	555	591.551152073733	-36.5511520737327
60	565	603.195391705069	-38.1953917050691
61	542	584.20737327189	-42.2073732718895

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/1368h1195682629.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/1368h1195682629.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/2f3q81195682629.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/2f3q81195682629.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/3lezx1195682629.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/3lezx1195682629.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/4rm601195682629.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/4rm601195682629.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/5hs7h1195682629.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/5hs7h1195682629.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/6q6wn1195682629.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/6q6wn1195682629.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/7eqa41195682629.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/7eqa41195682629.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/8mxmc1195682630.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/8mxmc1195682630.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/99wf31195682630.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682241mywrjtolkrpxkqw/99wf31195682630.ps (open in new window)

Parameters:

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice)

par1 <- as.numeric(par1)

x <- t(y)

k <- length(x[1,])

n <- length(x[,1])

x1 <- cbind(x[,par1], x[,1:k!=par1])

mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])

colnames(x1) <- mycolnames #colnames(x)[par1]

x <- x1

if (par3 == 'First Differences'){

x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))

for (i in 1:n-1) {

for (j in 1:k) {

x2[i,j] <- x[i+1,j] - x[i,j]

}

}

x <- x2

}

if (par2 == 'Include Monthly Dummies'){

x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))

for (i in 1:11){

x2[seq(i,n,12),i] <- 1

}

x <- cbind(x, x2)

}

if (par2 == 'Include Quarterly Dummies'){

x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))

for (i in 1:3){

x2[seq(i,n,4),i] <- 1

}

x <- cbind(x, x2)

}

k <- length(x[1,])

if (par3 == 'Linear Trend'){

x <- cbind(x, c(1:n))

colnames(x)[k+1] <- 't'

}

x

k <- length(x[1,])

df <- as.data.frame(x)

(mylm <- lm(df))

(mysum <- summary(mylm))

bitmap(file='test0.png')

plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')

points(x[,1]-mysum$resid)

grid()

dev.off()

bitmap(file='test1.png')

plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')

grid()

dev.off()

bitmap(file='test2.png')

hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')

grid()

dev.off()

bitmap(file='test3.png')

densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')

dev.off()

bitmap(file='test4.png')

qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')

grid()

dev.off()

(myerror <- as.ts(mysum$resid))

bitmap(file='test5.png')

dum <- cbind(lag(myerror,k=1),myerror)

dum

dum1 <- dum[2:length(myerror),]

dum1

z <- as.data.frame(dum1)

z

plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')

lines(lowess(z))

abline(lm(z))

grid()

dev.off()

bitmap(file='test6.png')

acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')

grid()

dev.off()

bitmap(file='test7.png')

pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')

grid()

dev.off()

bitmap(file='test8.png')

opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))

plot(mylm, las = 1, sub='Residual Diagnostics')

par(opar)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)

a<-table.row.end(a)

myeq <- colnames(x)[1]

myeq <- paste(myeq, '[t] = ', sep='')

for (i in 1:k){

if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')

myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')

if (rownames(mysum$coefficients)[i] != '(Intercept)') {

myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')

if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')

}

}

myeq <- paste(myeq, ' + e[t]')

a<-table.row.start(a)

a<-table.element(a, myeq)

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable1.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Variable',header=TRUE)

a<-table.element(a,'Parameter',header=TRUE)

a<-table.element(a,'S.D.',header=TRUE)

a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)

a<-table.element(a,'2-tail p-value',header=TRUE)

a<-table.element(a,'1-tail p-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:k){

a<-table.row.start(a)

a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)

a<-table.element(a,mysum$coefficients[i,1])

a<-table.element(a, round(mysum$coefficients[i,2],6))

a<-table.element(a, round(mysum$coefficients[i,3],4))

a<-table.element(a, round(mysum$coefficients[i,4],6))

a<-table.element(a, round(mysum$coefficients[i,4]/2,6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable2.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple R',1,TRUE)

a<-table.element(a, sqrt(mysum$r.squared))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'R-squared',1,TRUE)

a<-table.element(a, mysum$r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Adjusted R-squared',1,TRUE)

a<-table.element(a, mysum$adj.r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (value)',1,TRUE)

a<-table.element(a, mysum$fstatistic[1])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[2])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[3])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'p-value',1,TRUE)

a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Residual Standard Deviation',1,TRUE)

a<-table.element(a, mysum$sigma)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Sum Squared Residuals',1,TRUE)

a<-table.element(a, sum(myerror*myerror))

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable3.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Time or Index', 1, TRUE)

a<-table.element(a, 'Actuals', 1, TRUE)

a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)

a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)

a<-table.row.end(a)

for (i in 1:n) {

a<-table.row.start(a)

a<-table.element(a,i, 1, TRUE)

a<-table.element(a,x[i])

a<-table.element(a,x[i]-mysum$resid[i])

a<-table.element(a,mysum$resid[i])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable4.tab')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by